Related papers: Games for Topological Fixpoint Logic
It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…
This note points out a lemma on closures of monotonic increasing functions and shows how it is applicable to decomposition and modularity for semantics defined as the least fixedpoint of some monotonic function. In particular it applies to…
The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…
The article is devoted to a structure of topological spaces related with topological quasigroups. Regular and complete spaces over topological quasigroups are studied. Separations and embeddings are also investigated for them. Their…
This book summarizes ongoing research introducing probability space isomorphic mappings into the strategy spaces of game theory. This approach is motivated by discrepancies between probability theory and game theory when applied to the same…
The topological classification of gapped band structures depends on the particular definition of topological equivalence. For translation-invariant systems, stable equivalence is defined by a lack of restrictions on the numbers of occupied…
We present three examples of \textit{multi-topological} semantics for intuitionistic modal logic with one modal operator $\Box$ (which behaves in some sense like necessity). We show that it is possible to treat neighborhood models,…
We introduce the notion of Local Computation Mechanism Design - designing game theoretic mechanisms which run in polylogarithmic time and space. Local computation mechanisms reply to each query in polylogarithmic time and space, and the…
Higher-Order Fixpoint Logic (HFL) is a hybrid of the simply typed \lambda-calculus and the modal \lambda-calculus. This makes it a highly expressive temporal logic that is capable of expressing various interesting correctness properties of…
We study properties of relational structures such as graphs that are decided by families of Boolean circuits. Circuits that decide such properties are necessarily invariant to permutations of the elements of the input structures. We focus…
Synchronous linear constraint system games are nonlocal games that verify whether or not two players share a solution to a given system of equations. Two algebraic objects associated to these games encode information about the existence of…
We introduce Value Coalition Logic, a typed assignment-based reconstruction of classical coalition logic. The strategic semantics is unchanged: coalitional ability is still interpreted by the standard one-step game-form clause. The change…
It is known that the model checking problem for the modal mu-calculus reduces to the problem of solving a parity game and vice-versa. The latter is realised by the Walukiewicz formulas which are satisfied by a node in a parity game iff…
Logic programming with tabling and constraints (TCLP, tabled constraint logic programming) has been shown to be more expressive and, in some cases, more efficient than LP, CLP, or LP with tabling. In this paper we provide insights regarding…
Game comonads offer a categorical view of a number of model-comparison games central to model theory, such as pebble and Ehrenfeucht-Fra\"iss\'e games. Remarkably, the categories of coalgebras for these comonads capture preservation of…
We define a fixed point action in two-dimensional lattice ${\rm CP}^{N-1}$ models. The fixed point action is a classical perfect lattice action, which is expected to show strongly reduced cutoff effects in numerical simulations.…
We introduce several methods of decomposition for two player normal form games. Viewing the set of all games as a vector space, we exhibit explicit orthonormal bases for the subspaces of potential games, zero-sum games, and their orthogonal…
In this paper we connect selection principles on a topological space to corresponding selection principles on one of its hyperspaces. We unify techniques and generalize theorems from the known results about selection principles for common…
This paper argues that the finite horizon paradox, where game theory contradicts intuition, stems from the limitations of standard number systems in modelling the cognitive perception of infinity. To address this issue, we propose a new…
Coordination games with explicit spatial or relational structure are of interest to economists, ecologists, sociologists, and others studying emergent global properties in collective behavior. When assemblies of individuals seek to…